Future work is manifold. Firstly, we aim to extend the equations of section
 to images e.g. using the kernel framework in
[1]} or developing a space-time method. We also
aim to find an explicit solution to the geodesic equations for \(\mathbf {p}\)  and
\(\mathbf {q}\)  and with the additional terms involving \(\nu \)  à la
[2]} to eliminate the need \(\nu \)  to be bounded from below.
Further, as outlined in  there
are many aspects of the probabilistic framework that need rigorous treatment.
Beyond the references therein, see also the work in [3]}.
Natural extensions of our probabilistic approach also include fully treating
\(\nu \)  as a function and interpreting the resulting inverse problem through the
appropriate measure-theoretical lens. Adding a time-dependency to \(\nu \)  can also
be explored. Determining a truncated Fourier series of \(\nu \)  could lead to
efficient numerical methods. More generally, we hope to reconcile our attempts
to model growth here with the mathematically elegant approach described in
[4]} and with the more general mathematics of growth
[5]}.
